Method and apparatus of image morphing and computer accessible storage medium thereof

ABSTRACT

An image morphing method is suitable for generating an intermediate image sequence. First, a control point CP={(p i ,q i )} i=1 . . . N  is specified and marked in a source image I s ({right arrow over (x)}) and a destination image I d ({right arrow over (x)}′). Next, an edge gradient parameter (I se ({right arrow over (x)}), I de ({right arrow over (x)}′) is computed according to the source image I s ({right arrow over (x)}) and the destination image I d ({right arrow over (x)}′). Next, a total objective function E(D f ,D b ) is computed according to the above-mentioned control point CP and edge gradient parameter (I se ({right arrow over (x)}), I de ({right arrow over (x)}′)). The above-mentioned intermediate image sequence is generated by using the total objective function E(D f ,D b ). The present invention utilizes the edge gradients of the source image I s ({right arrow over (x)}) and the destination image I d ({right arrow over (x)}′) to enhance the constraint of image morphing. Thus, the image morphing effect is promoted.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the priority benefit of P.R.C. applicationserial no. 200710102155.6, filed on Apr. 29, 2007. All disclosure of theP.R.C. application is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to a method for processingmultimedia, and more particularly, to an image processing method.

2. Description of Related Art

Image morphing technique is a technique regarding dynamically morphingan image gradually into another image by cross-fading and warping. Thetechnique is broadly applicable to multimedia fields, such as animatedcartoon, computer-generated animation technique and processing forspecial movie effects.

The image morphing technique today is mainly implemented by an operator,who manually defines and marks some control points on a source image anda destination image so as to constrain the geometric deformations ofother points by means of the control points, and conducts geometricinterpolations to obtain an intermediate image sequence from the sourceimage to the destination image.

The conventional image morphing method is implemented only by anoperator to manually define and mark some control points on a sourceimage and a destination image for calculating geometric mapping betweenimages, wherein if the defined control points are too dense, the jobburden for an operator to manually mark would be largely increased, inaddition to more faults during operating. If the control points are toofew however, serious geometric distortions would likely occur at thosepixel points far away from a control point in the image.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to an image morphingmethod and an image morphing apparatus suitable for generating anintermediate image sequence to promote the dynamic morphing effect usedin multimedia fields.

The present invention provides an image morphing method suitable forgenerating an intermediate image sequence. First, a set of controlpoints (morph points, or markers) CP={(p_(i),q_(i))}_(i=1 . . . N) ismarked respectively in a source image I_(s)({right arrow over (x)}) anda destination image I_(d)({right arrow over (x)}′). Next, an edgegradient parameter (I_(se)({right arrow over (x)}), I_(de)({right arrowover (x)}′)) is computed according to the source image I_(s)({rightarrow over (x)}) and the destination image I_(d)({right arrow over(x)}′). Then, a total objective function E(D^(f),D^(b)) is computedaccording to the above-mentioned control points CP and theabove-mentioned edge gradient parameter (I_(se)({right arrow over (x)}),I_(de)({right arrow over (x)}′)). Further, the above-mentionedintermediate image sequence I_(i)({right arrow over(x)})=α_(i)I_(si)({right arrow over (x)})+(1−α_(i))I_(dj)({right arrowover (x)}) is generated by using the above-mentioned total objectivefunction E(D^(f),D^(b)).

The present invention also provides an image morphing method suitablefor generating an intermediate image sequence. First, an edge gradientparameter (I_(se)({right arrow over (x)}), I_(de)({right arrow over(x)}′)) is computed according to a source image I_(s)({right arrow over(x)}) and a destination image I_(d)({right arrow over (x)}′). Then, atotal objective function E(D^(f),D^(b)) is computed according to theedge gradient parameter (I_(se)({right arrow over (x)}), I_(de)({rightarrow over (x)}′)). Further, the above-mentioned intermediate imagesequence I_(i)({right arrow over (x)})=α_(i)I_(si)({right arrow over(x)})+(1−α_(i))I_(dj)({right arrow over (x)}) is generated by using theabove-mentioned total objective function E(D^(f),D^(b)).

The present invention also provides an apparatus of generatingintermediate image sequence to morph images. The apparatus receives asource image and a destination image, and includes a unit of specifyingand marking control points, a unit of computing edge gradient parameter,a unit of computing total objective function and a unit of generatingintermediate image sequence. The unit of specifying and marking controlpoints respectively in the source image and the destination imagespecifies and marks at least a control point. The unit of computing edgegradient parameter computes an edge gradient parameter according to thesource image and the destination image. The unit of computing totalobjective function computes a total objective function according to atleast one of the control points and the edge gradient parameter. Theunit of generating intermediate image sequence generates theintermediate image sequence according to the total objective function.

The present invention also provides an apparatus of generatingintermediate image sequence to morph images. The apparatus receives asource image and a destination image, and includes a unit of computingedge gradient parameter, a unit of computing total objective functionand a unit of generating intermediate image sequence. The unit ofcomputing edge gradient parameter computes an edge gradient parameteraccording to the source image and the destination image. The unit ofcomputing total objective function computes a total objective functionaccording to the edge gradient parameter. The unit of generatingintermediate image sequence generates the intermediate image sequenceaccording to the total objective function.

According to the embodiments of the present invention, theabove-mentioned image morphing method utilizes the edge gradients of thesource image I_(s)({right arrow over (x)}) and the destination imageI_(d)({right arrow over (x)}′) to enhance image morphing constraint toadvance the image morphing effect.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the invention, and are incorporated in and constitute apart of this specification. The drawings illustrate embodiments of theinvention and, together with the description, serve to explain theprinciples of the invention.

FIG. 1 is a flowchart showing the steps of image morphing methodaccording to an embodiment of the present invention.

FIG. 2 is a flowchart showing the step of computing an edge gradientparameter according to an embodiment of the present invention.

FIG. 3 is a flowchart showing the step of computing a total objectivefunction according to an embodiment of the present invention.

FIG. 4 is a flowchart showing the step of computing a forward objectivefunction according to an embodiment of the present invention.

FIG. 5 is a flowchart showing the step of computing a backward objectivefunction according to an embodiment of the present invention.

FIG. 6 is a flowchart showing the step of generating an intermediateimage sequence according to an embodiment of the present invention.

FIG. 7 includes diagrams respectively showing an intermediate imagesequence considering edge constraint and an intermediate image sequencewithout considering edge constraint according to an embodiment of thepresent invention.

FIG. 8 is a flowchart showing the steps of image morphing methodaccording to another embodiment of the present invention.

FIG. 9 is a flowchart showing the step of computing a total objectivefunction according to another embodiment of the present invention.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the present preferredembodiments of the invention, examples of which are illustrated in theaccompanying drawings. Wherever possible, the same reference numbers areused in the drawings and the description to refer to the same or likeparts.

Among all elements of an image, the edges of the image carry over 80% ofthe total information. When an image is morphed into another image, themost important is how many edge line segments can be smoothly morphedinto the corresponding edges in another morphed image, which nearlydetermines the effectiveness of the used algorithm and the performanceof the finally generated intermediate image sequence. Therefore, amapping between edges in a source image and the corresponding edges in adestination image often serves as an important constraint for modifyinga morphing algorithm, which would largely promote the robustness of theabove-mentioned algorithm and the performance of an intermediate imagesequence.

Accordingly, the present invention induces a concept of edge constraintinto the conventional image morphing method, where the correspondencesbetween the edge points in a source image and the correspondingdestination image are fully regarded for computing the geometricmappings between the source image I_(s)({right arrow over (x)}) and thedestination imaged I_(d)({right arrow over (x)}′). That is to say, thepixels on an edge of the source image I_(s)({right arrow over (x)})should correspond to the pixels of the corresponding edge of thedestination image I_(d)({right arrow over (x)}′) to the fullest extent.

FIG. 1 is a flowchart showing the steps of image morphing methodaccording to an embodiment of the present invention. Referring to FIG.1, first as shown by step S110, a set of control pointsCP={(p_(i),q_(i))}_(i=1 . . . N) is specified and marked. Next in stepS120, edge gradient parameters (I_(se)({right arrow over (x)}),I_(de)({right arrow over (x)}′)) is computed according to the sourceimage I_(s)({right arrow over (x)}) and the destination imageI_(d)({right arrow over (x)}′). Then in step S130, a total objectivefunction E(D^(f),D^(b)) is computed by using the control points CP, thesource image edge gradient I_(se)({right arrow over (x)}) and thedestination image edge gradient I_(de)({right arrow over (x)}′). Furtherin step S140, an intermediate image sequence is generated by using thetotal objective function E(D^(f),D^(b)).

Referring to FIG. 2, the above-mentioned step S120 in an embodiment ofthe present invention includes computing the edge gradient of the sourceimage I_(s)({right arrow over (x)}) to obtain a source image edgegradient I_(se)({right arrow over (x)}), (step S121) and computing theedge gradient of the destination image I_(d)({right arrow over (x)}′) toobtain a destination image edge gradient I_(de)({right arrow over(x)}′), (step S122) wherein the source image edge gradient can beexpressed in I_(se)({right arrow over(x)})=∇_({right arrow over (x)})(I_(s)({right arrow over (x)})), whilethe destination image edge gradient can be expressed in I_(de)({rightarrow over (x)}′)=∇_({right arrow over (x)}′)(I_(d)({right arrow over(x)}′)).

Referring to FIG. 3, the above-mentioned step S130 in an embodiment ofthe present invention includes computing the total objective function byE(D^(f),D^(b))=E^(f)(D^(f))+E^(b)(D^(b))+Dis(D^(b),D^(f)), wherein thetotal objective function E(D^(f),D^(b)) includes a forward objectivefunction E^(f)(D^(f)) (step S131), a backward objective functionD^(b)({right arrow over (x)}′) (step S135) and an objective function ofdeviation values Dis(D^(b),D^(f)) (step S139), wherein the forwardobjective function E^(f)(D^(f)) has physical meaning as follows:

Assuming a geometric morphing function from the source imageI_(s)({right arrow over (x)}) to the destination image I_(d)({rightarrow over (x)}′) is D^(f)({right arrow over (x)}), and D^(f)({rightarrow over (x)}) is termed as a forward morphing function whichrepresents a mapping from every point in the source image I_(s)({rightarrow over (x)}) to the destination image I_(d)({right arrow over (x)}′)and is expressed by D^(f)({right arrow over (x)})={d^(f)({right arrowover (x)})|d^(f)({right arrow over (x)})=(u,v)}. The objective of theforward morphing is a function of the forward morphing functionD^(f)({right arrow over (x)}), i.e. forward objective functionE^(f)(D^(f)).

Similarly, the backward objective function D^(b)({right arrow over(x)}′) has physical meaning as follows:

Assuming a geometric morphing function from the destination imageI_(d)({right arrow over (x)}′) to the source image I_(s)({right arrowover (x)}) is D^(b)({right arrow over (x)}′), and D^(b)({right arrowover (x)}′) is termed as a backward morphing function which represents amapping from every point in the destination image I_(d)({right arrowover (x)}′) to the source image I_(s)({right arrow over (x)}) and isexpressed by D^(b)({right arrow over (x)})={d^(b)({right arrow over(x)})|d^(b)({right arrow over (x)})=(u′,v′)}. The objective of thebackward morphing is a function of the backward morphing functionD^(b)({right arrow over (x)}′),i.e. backward objective functionE^(b)(D^(b)).

The objective function of deviation values Dis(D^(b),D^(f)) is thedistance of the backward morphing function D^(b)({right arrow over(x)}′) from the forward morphing function D^(f)({right arrow over (x)}),which reflects a deviation between the forward geometric morphing andthe backward geometric morphing and is defined by:

${{{Dis}\left( {D^{b},D^{j}} \right)} = {{\sum\limits_{x^{\prime}}{\rho_{dis}\left( {{d^{b}\left( {\overset{\rightarrow}{x}}^{\prime} \right)} - {d^{f}\left( {{\overset{\rightarrow}{x}}^{\prime} + {d^{b}\left( {\overset{\rightarrow}{x}}^{\prime} \right)}} \right)}} \right)}} + {\sum\limits_{x^{\prime}}{\rho_{dis}\left( {{d^{f}\left( \overset{\rightarrow}{x} \right)} - {d^{b}\left( {\overset{\rightarrow}{x} + {d^{f}\left( \overset{\rightarrow}{x} \right)}} \right)}} \right)}}}},$

wherein ρ_(dis)({right arrow over (x)}₁,{right arrow over(x)}₂)=min(λ_(dis)∥{right arrow over (x)}₁−{right arrow over(x)}₂∥,T_(dis)).

Referring to FIG. 4, in an embodiment of the present invention, forwardobjective function E^(f)(D^(f)) includes an objective of control pointE_(cp)(D) (step S132), an objective of forward edge gradient E_(edge)^(f) (step S133) and an objective of smoothness E_(s)(D) (step S134).

The algorithm of the objective of control point E_(cp)(D) is as follows:

Assuming N pairs of control points in the source image I_(s)({rightarrow over (x)}) and the destination image I_(d)({right arrow over(x)}′) are CP={(p_(i),q_(i))}_(i=1 . . . N) and defining

${\overset{\rightarrow}{t}\left( \overset{\rightarrow}{x} \right)} = \left\{ {{\begin{matrix}\left( {{\overset{\rightarrow}{q}}_{k} - {\overset{\rightarrow}{p}}_{k}} \right) & {{{if}\mspace{14mu} \overset{\rightarrow}{x}} = {\overset{\rightarrow}{p}}_{k}} \\{\sum\limits_{i = 1}^{N}{{w_{i}\left( \overset{\rightarrow}{x} \right)}\left( {{\overset{\rightarrow}{q}}_{i} - {\overset{\rightarrow}{p}}_{i}} \right)}} & {else}\end{matrix}{w_{i}\left( \overset{\rightarrow}{x} \right)}} = {{1/{{\overset{\rightarrow}{x} - {\overset{\rightarrow}{p}}_{i}}}}{\sum\limits_{i = 1}^{N}\frac{1}{{\overset{\rightarrow}{x} - {\overset{\rightarrow}{p}}_{i}}}}}} \right.$

wherein {right arrow over (t)}({right arrow over (x)}) represents thedisplacement vector of each point in source image I_(s)({right arrowover (x)}) or destination image I_(d)({right arrow over (x)}′) whentaking account of a control point CP only; then w_(i)({right arrow over(x)}) represents an influence factor of a control point CP on regularimage points. The objective of control point E_(cp)(D) is defined by

${{E_{cp}(D)} = {\sum\limits_{\overset{\rightarrow}{x}}^{\;}{\rho_{cp}\left( {{\overset{\rightarrow}{d}\left( \overset{\rightarrow}{x} \right)},{\overset{\rightarrow}{t}\left( \overset{\rightarrow}{x} \right)}} \right)}}},$

wherein ρ_(cp)({right arrow over (a)},{right arrow over(b)})=min(λ_(cp)∥{right arrow over (a)}−{right arrow over (b)}∥,T_(cp))and ρ_(cp) is an amplitude-limited distance function.

The algorithm of the objective of forward edge gradient E_(edge) ^(f) isas follows:

The objective of forward edge gradient E_(edge) ^(f) is defined by

${{E_{edge}^{f}\left( D^{f} \right)} = {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{edge}\left( {{I_{se}\left( \overset{\rightarrow}{x} \right)} - {I_{de}\left( {\overset{\rightarrow}{x} + {{\overset{\rightarrow}{d}}^{f}\left( \overset{\rightarrow}{x} \right)}} \right)}} \right)}}},$

wherein ρ_(edge)(s)=min(λ_(edge)|s|,T_(edge)) and ρ_(edge) is anamplitude-limited function.

The algorithm of the objective of smoothness E_(s)(D) is as follows:

Assuming each point in the image is s, which has a 3×3 neighbouringdomain N(s) and defining C={s,t|s<t,tεN(s)} representing the pair numberof adjacent points to s in the neighbouring domain, then the objectiveof smoothness E_(s)(D) is defined by

${{E_{s}(D)} = {\sum\limits_{s,{t \in C}}{\lambda_{s}{{\left( {s + {d(s)}} \right) - \left( {t + {d(t)}} \right)}}}}},$

wherein λ_(s) is the weight of the objective of smoothness E_(s)(D).Note that the present invention does not limit the neighbouring domainN(s) of a point s to only 3×3, in fact, N(s) can be a m×m neighbouringdomain where m is a positive integer greater than or equal to 3, whichis still within the scope of the present invention. Moreover, thepresent invention can cover other non-square neighbouring domains wherea smooth computation over the neighbouring domains of each point in theimage is performed, and thus non-square neighbouring domains are withinthe scope of the present invention.

Similarly as shown by FIG. 5, in an embodiment of the present invention,backward objective function E^(b)(D^(b)) includes an objective ofcontrol point E_(cp)(D) (step S136), an objective of backward edgegradient E_(edge) ^(b) (step S137) and an objective of smoothnessE_(s)(D) (step S138), wherein the objective of backward edge gradientE_(edge) ^(b) is computed by

${E_{edge}^{b}\left( D^{b} \right)} = {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{edge}\left( {{I_{de}\left( \overset{\rightarrow}{x} \right)} - {I_{se}\left( {\overset{\rightarrow}{x} + {{\overset{\rightarrow}{d}}^{b}\left( \overset{\rightarrow}{x} \right)}} \right)}} \right)}}$

and ρ_(edge)(s)=min(λ_(edge)|s|,T_(edge)). The above-mentioned objectiveof forward edge gradient E_(edge) ^(f) and the objective of backwardedge gradient E_(edge) ^(f) reflects that the edge points in the sourceimage I_(s)({right arrow over (x)}) (the image where the morphing beginswith) should correspond to the edge points in the destination imageI_(d)({right arrow over (x)}′) (the image where the morphing is ended)to the fullest extent so as to ensure a good visual quality of anintermediate image sequence generated by morphing. In terms of thealgorithm, an edge objective means the minimum of sums of all gradientdifferences between each pair of corresponding pixel points in aspecific geometric transformation, and the edge objective is a novelconcept provided by the present invention.

After obtaining the total objective function E(D^(f),D^(b)), in stepS140, a computation is conducted on the total objective functionE(D^(f),D^(b)) to obtain the intermediate image sequence. Referring toFIG. 6, first in step S141, the total objective function E(D^(f),D^(b))is optimized to obtain a specific forward morphing function

^(f) and a specific backward morphing function

^(b). In fact, the specific forward morphing function

^(f) and the specific backward morphing function

^(b) are respectively the forward morphing function D^(f)({right arrowover (x)}) and the backward morphing function D^(b)({right arrow over(x)}) in relation to the total objective function E(D^(f),D^(b)). Thereare many approaches for optimizing the total objective functionE(D^(f),D^(b)), for example, belief propagation algorithm, annealingalgorithms and genetic algorithm.

After obtaining the specific forward morphing function

^(f) and the specific backward morphing function

^(b), further, by using the obtained

^(f) to conduct an interpolation operation on the source imageI_(s)({right arrow over (x)}) a forward transition image sequenceI_(si)({right arrow over (x)}) is generated (step S142); by using the

^(b) to conduct an interpolation operation on the destination imageI_(d)({right arrow over (x)}′), a backward transition image sequenceI_(d)({right arrow over (x)}′) is generated (step S143). Furthermore,the forward transition image sequence I_(si)({right arrow over (x)}) andthe backward transition image sequence I_(di)({right arrow over (x)}′)are used to conduct a color-blending operation so as to generate theintermediate image sequence, which is implemented as follows:

The intermediate image sequence can be I_(i)({right arrow over(x)})=α_(i)I_(si)({right arrow over (x)})+(1−α_(i))I_(dj)({right arrowover (x)}), (i=1, 2 . . . N), wherein α_(i)=1−i/N, which represents aweight factor of color-blending.

Note that if the source image I_(s)({right arrow over (x)}) is quitesimilar to the destination image I_(d)({right arrow over (x)}′), theintermediate image sequence may include an image only, which is alsoconstrued to be within the scope of the present invention.

The objective of control point E_(cp)(D) represents the constraint ofthe specified and marked control point on a geometric transformationfunction. The objective of forward edge gradient E_(edge) ^(f) and theobjective of backward edge gradient E_(edge) ^(b) are used to measurethe mapping extent of the edge information between the source imageI_(s)({right arrow over (x)}) and the destination image I_(d)({rightarrow over (x)}′) in the geometric transformation. The objective ofsmoothness E_(s)(D) represents whether the geometric transformation inthe space is smooth.

The objective of forward edge gradient E_(edge) ^(f) and the objectiveof backward edge gradient E_(edge) ^(b) are the novel ideas provided bythe present invention. Taking FIG. 7 as an example, when the structuresof the source image (a) and the destination image (b) are simpler, thecontrol points specified and marked control points in the source image(a) and the destination image (b) are usually located at four corners ofthe square. However, from the point of view of the objective of forwardedge gradient E_(edge) ^(f) and the objective of backward edge gradientE_(edge) ^(b), the color differences between the square of the sourceimage (a) and the circle of the destination image (b) are significant,i.e., the square of the source image (a) and the circle of thedestination image (b) have great gradients at the edges thereof,therefore, the physical meaning to consider the objective of forwardedge gradient edge and the objective of backward edge gradient edge restin that an indefinitely large number of control points are specified andmarked on the edges of the source image (a) and the destination image(b) instead of four corners of the square of the source image (a).

Thus it can be seen from FIG. 7, the morphing performance of anintermediate image sequence considering edge constraint is more superiorthan that without considering edge constraint. The image morphing methodconsidering edge constraint even allows to omit a step of specifying andmarking control points, because the locations where the greatest changeof edge gradient for an image occurs are almost the most preferredlocations for manually specifying and marking control points.

FIG. 8 is a flowchart showing the steps of image morphing method withoutmanually specifying and marking control points according to anotherembodiment of the present invention. Referring to FIG. 8, the steps S210and S230 of the present embodiment are respectively similar to the stepsS120 and S140 of the above-mentioned embodiment. Referring to FIG. 9,the step of computing a total objective function E(D^(f),D^(b)) in anembodiment of the present invention is similar to the step S130 of theabove-mentioned embodiment except for omitting the step of computingobjective of control point E_(cp)(D). The implementation detail of thestep S220 of the embodiment can be referred to the above embodiment anddetail description thereof is omitted for simplicity.

In the embodiment, there is no operation of manually specifying andmarking control points; instead, the embodiment only uses the objectiveof forward edge gradient E_(edge) ^(f) and the objective of smoothnessE_(s)(D) to determine the forward objective function E^(f)(D^(f)) anduses the objective of backward edge gradient E_(edge) ^(b) and theobjective of smoothness E_(s)(D) to determine the backward objectivefunction E^(b)(D^(b)). Moreover in another embodiment of the presentinvention, only the objective of forward edge gradient E_(edge) ^(f) isused to determine the forward objective function E^(f)(D^(f)) and theobjective of backward edge gradient E_(edge) ^(b) used to determine thebackward objective function E^(b)(D^(b)). The unique point of thepresent embodiment rests in entirely dismissing the step of manuallyspecifying and marking control points, which makes the method ofgenerating an intermediate image sequence entirely automated.

In summary, the present invention has at least the following advantages:

1. By inducing the constraint of image edge gradient, the presentinvention largely lower the number of manually-marking control points ofan operator, which lightens the operator burden.

2. For a same number of control points an operator specifies and marks,compared to the prior art, the quality of a generated intermediate imagesequence cane be significantly promoted.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the structure of the presentinvention without departing from the scope or spirit of the invention.In view of the foregoing, it is intended that the present inventioncover modifications and variations of this invention provided they fallwithin the scope of the following claims and their equivalents.

1. An image morphing method, suitable for generating an intermediateimage sequence, comprising: computing an edge gradient parameter(I_(se)({right arrow over (x)}), I_(de)({right arrow over (x)}′)according to a source image I_(s)({right arrow over (x)}) and adestination image I_(d)({right arrow over (x)}′); computing a totalobjective function E(D^(f),D^(b)) according to the edge gradientparameter (I_(se)({right arrow over (x)}), I_(de)({right arrow over(x)}′)); and generating the intermediate image sequence according to thetotal objective function E(D^(f),D^(b)).
 2. The image morphing methodaccording to claim 1, wherein the edge gradient parameter (I_(se)({rightarrow over (x)}), I_(de)({right arrow over (x)}′)) comprises a sourceimage edge gradient I_(se)({right arrow over (x)}) and a destinationimage edge gradient I_(de)({right arrow over (x)}′), and the step ofcomputing the edge gradient parameter (I_(se)({right arrow over (x)}),I_(de)({right arrow over (x)}′)) comprises: computing the source imageedge gradient I_(se)({right arrow over (x)}) according to the sourceimage I_(s)({right arrow over (x)}), wherein I_(se)({right arrow over(x)})=∇_({right arrow over (x)})(I_(s)({right arrow over (x)})); andcomputing the destination image edge gradient I_(de)({right arrow over(x)}′) according to the destination image I_(d)({right arrow over(x)}′), wherein I_(de)({right arrow over(x)}′)=∇_({right arrow over (x)}′)(I_(d)({right arrow over (x)}′)). 3.The image morphing method according to claim 1, wherein the totalobjective function E(D^(f),D^(b)) comprises: a forward objectivefunction E^(f)(D^(f)), wherein the forward objective functionE^(f)(D^(f)) is the objective of a forward morphing functionD^(f)({right arrow over (x)}); a backward objective functionE^(b)(D^(b)), wherein the backward objective function E^(b)(D^(b)) isthe objective of a backward morphing function D^(b)({right arrow over(x)}′); and an objective function of deviation values Dis(D^(b),D^(f)),wherein the objective function of deviation values Dis(D^(b),D^(f)) is adistance between the forward morphing function D^(f)({right arrow over(x)}) and the backward morphing function D^(b)({right arrow over (x)}′).4. The image morphing method according to claim 3, wherein the objectivefunction of deviation values is defined by${{Dis}\left( {D^{b},D^{f}} \right)} = {{\sum\limits_{{\overset{\rightarrow}{x}}^{\prime}}{\rho_{dis}\left( {{d^{b}\left( {\overset{\rightarrow}{x}}^{\prime} \right)} - {d^{f}\left( {{\overset{\rightarrow}{x}}^{\prime} + {d^{b}\left( {\overset{\rightarrow}{x}}^{\prime} \right)}} \right)}} \right)}} + {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{dis}\left( {{d^{f}\left( \overset{\rightarrow}{x} \right)} - {d^{b}\left( {\overset{\rightarrow}{x} + {d^{f}\left( \overset{\rightarrow}{x} \right)}} \right)}} \right)}}}$and ρ_(dis)({right arrow over (x)}₁,{right arrow over(x)}₂)=min(λ_(dis)∥{right arrow over (x)}₁−{right arrow over(x)}₂∥,T_(dis)).
 5. The image morphing method according to claim 3,wherein the forward objective function E^(f)(D^(f)) comprises: anobjective of forward edge gradient E_(edge) ^(f), wherein a parameter ofthe objective of forward edge gradient E_(edge) ^(f) comprises the edgegradient parameter (I_(se)({right arrow over (x)}), I_(de)({right arrowover (x)}′)).
 6. The image morphing method according to claim 5, whereincomputing the objective of forward edge gradient E_(edge) ^(f) comprises${{E_{edge}^{f}\left( D^{f} \right)} = {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{edge}\left( {{I_{se}\left( \overset{\rightarrow}{x} \right)} - {I_{de}\left( {\overset{\rightarrow}{x} + {{\overset{\rightarrow}{d}}^{f}\left( \overset{\rightarrow}{x} \right)}} \right)}} \right)}}},$wherein ρ_(edge)(s)=min(λ_(edge)|s|,T_(edge)).
 7. The image morphingmethod according to claim 3, wherein the forward objective functionE^(f)(D^(f)) comprises an objective of smoothness E_(s)(D).
 8. The imagemorphing method according to claim 7, wherein the step of computing theobjective of smoothness E_(s)(D) comprises: assuming s is any one pointin the image and N(s) is an m×m neighbouring domain of s, and definingC={s,t|s<t,tεN(s)} to represent the pair number of adjacent points to sin the neighbouring domain, the objective of smoothness E_(s)(D) isdefined by${{E_{s}(D)} = {\sum\limits_{s,{t \in C}}{\lambda_{s}{{\left( {s + {d(s)}} \right) - \left( {t + {d(t)}} \right)}}}}},$wherein λ_(s) is a weight of the objective of smoothness E_(s)(D) in theforward objective function E^(f)(D^(f)), and m is a positive integergreater than or equal to
 3. 9. The image morphing method according toclaim 3, wherein the backward objective function E^(b)(D^(b)) comprises:an objective of backward edge gradient E_(edge) ^(b), wherein theparameter of the objective of backward edge gradient E_(edge) ^(b)comprises the edge gradient parameter (I_(se)({right arrow over (x)}),I_(de)({right arrow over (x)}′)).
 10. The image morphing methodaccording to claim 9, wherein the step of computing the objective ofbackward edge gradient E_(edge) ^(b) comprises:${{E_{edge}^{b}\left( D^{b} \right)} = {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{edge}\left( {{I_{de}\left( \overset{\rightarrow}{x} \right)} - {I_{se}\left( {\overset{\rightarrow}{x} + {{\overset{\rightarrow}{d}}^{b}\left( \overset{\rightarrow}{x} \right)}} \right)}} \right)}}},$wherein ρ_(edge)(s) min(λ_(edge)|s|,T_(edge)).
 11. The image morphingmethod according to claim 3, wherein the backward objective functionE^(b)(D^(b)) comprises an objective of smoothness E_(s)(D).
 12. Theimage morphing method according to claim 11, wherein the step ofcomputing the objective of smoothness E_(s)(D) comprises: assuming s isany one point in the image and N(s) is an m×m neighbouring domain of s,and defining C={s,t|s<t,tεN(s)} to represent a pair number of adjacentpoints to s in a neighbouring domain, then the objective of smoothnessE_(s)(D) is defined by${{E_{s}(D)} = {\sum\limits_{s,{t \in C}}{\lambda_{s}{{\left( {s + {d(s)}} \right) - \left( {t + {d(t)}} \right)}}}}},$wherein λ_(s) is the weigh of the objective of smoothness E_(s)(D) inthe backward objective function E^(b)(D^(b)), and m is a positiveinteger greater than or equal to
 3. 13. The image morphing methodaccording to claim 1, further comprising: specifying and marking atleast a control point CP={(p_(i),q_(i))}_(i=1 . . . N) in a source imageI_(s)({right arrow over (x)}) and a destination image I_(d)({right arrowover (x)}′).
 14. The image morphing method according to claim 5, furthercomprising: specifying and marking at least a control pointCP={(p_(i),q_(i))}_(i=1 . . . N) in a source image I_(s)({right arrowover (x)}) and a destination image I_(d)({right arrow over (x)}′);wherein the forward objective function E^(f)(D^(f)) comprises anobjective of control point E_(cp)(D), wherein a parameter of theobjective of control point E_(cp)(D) comprises the control point CP. 15.The image morphing method according to claim 14, wherein the step ofcomputing the objective of control point E_(cp)(D) comprises: defining${\overset{\rightarrow}{t}\left( \overset{\rightarrow}{x} \right)} = \left\{ {{\begin{matrix}\left( {{\overset{\rightarrow}{q}}_{k} - {\overset{\rightarrow}{p}}_{k}} \right) & {{{if}\mspace{14mu} \overset{\rightarrow}{x}} = {\overset{\rightarrow}{p}}_{k}} \\{\sum\limits_{i = 1}^{N}{{w_{i}\left( \overset{\rightarrow}{x} \right)}\left( {{\overset{\rightarrow}{q}}_{i} - {\overset{\rightarrow}{p}}_{i}} \right)}} & {else}\end{matrix}{w_{i}\left( \overset{\rightarrow}{x} \right)}} = {{1/{{\overset{\rightarrow}{x} - {\overset{\rightarrow}{p}}_{i}}}}{\sum\limits_{i = 1}^{N}\frac{1}{{\overset{\rightarrow}{x} - {\overset{\rightarrow}{p}}_{i}}}}}} \right.$wherein {right arrow over (t)}({right arrow over (x)}) represents thedisplacement vector of each point in the source image I_(s)({right arrowover (x)}) when taking account of the control point CP only;w_(i)({right arrow over (x)}) represents an influence factor of thecontrol point CP on regular image points; an objective of control pointE_(cp)(D) is defined by${{E_{cp}(D)} = {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{cp}\left( {{\overset{\rightarrow}{d}\left( \overset{\rightarrow}{x} \right)},{\overset{\rightarrow}{t}\left( \overset{\rightarrow}{x} \right)}} \right)}}},$wherein ρ_(cp)({right arrow over (a)},{right arrow over(b)})=min(λ_(cp)∥{right arrow over (a)}−{right arrow over (b)}∥,T_(cp))and ρ_(cp) is an amplitude-limited distance function; and computing anobjective of forward edge gradient E_(edge) ^(f) comprising${{E_{edge}^{f}\left( D^{f} \right)} = {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{edge}\left( {{I_{se}\left( \overset{\rightarrow}{x} \right)} - {I_{de}\left( {\overset{\rightarrow}{x} + {{\overset{\rightarrow}{d}}^{f}\left( \overset{\rightarrow}{x} \right)}} \right)}} \right)}}},$wherein ρ_(edge)(s)=min(λ_(edge)|s|,T_(edge)).
 16. The image morphingmethod according to claim 9, further comprising: specifying and markingat least a control point CP={(p_(i),q_(i))}_(i=1 . . . N) in a sourceimage I_(s)({right arrow over (x)}) and a destination image I_(d)({rightarrow over (x)}′); wherein the backward objective function E^(b)(D^(b))comprises an objective of control point E_(cp)(D), wherein the parameterof the objective of control point E_(cp)(D) comprises the control pointCP and an objective of backward edge gradient E_(edge) ^(b), wherein aparameter of the objective of backward edge gradient E_(edge) ^(b)comprises the edge gradient parameter (I_(se)({right arrow over (x)}),I_(de)({right arrow over (x)}′)).
 17. The image morphing methodaccording to claim 16, wherein computing the objective of control pointE_(cp)(D) comprises: defining${\overset{\rightarrow}{t}\left( \overset{\rightarrow}{x} \right)} = \left\{ {{\begin{matrix}\left( {{\overset{\rightarrow}{q}}_{k} - {\overset{\rightarrow}{p}}_{k}} \right) & {{{if}\mspace{14mu} \overset{\rightarrow}{x}} = {\overset{\rightarrow}{p}}_{k}} \\{\sum\limits_{i = 1}^{N}{{w_{i}\left( \overset{\rightarrow}{x} \right)}\left( {{\overset{\rightarrow}{q}}_{i} - {\overset{\rightarrow}{p}}_{i}} \right)}} & {else}\end{matrix}{w_{i}\left( \overset{\rightarrow}{x} \right)}} = {{1/{{\overset{\rightarrow}{x} - {\overset{\rightarrow}{p}}_{i}}}}{\sum\limits_{i = 1}^{N}\frac{1}{{\overset{\rightarrow}{x} - {\overset{\rightarrow}{p}}_{i}}}}}} \right.$wherein {right arrow over (t)}({right arrow over (x)}) represents thedisplacement vector of each point in the destination image when takingaccount of the control point CP only; w_(i)({right arrow over (x)})represents an influence factor of the control point CP on regular imagepoints; the objective of control point E_(cp)(D) is defined by${{E_{cp}(D)} = {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{cp}\left( {{\overset{\rightarrow}{d}\left( \overset{\rightarrow}{x} \right)},{\overset{\rightarrow}{t}\left( \overset{\rightarrow}{x} \right)}} \right)}}},$wherein ρ_(cp)({right arrow over (a)},{right arrow over(b)})=min(λ_(cp)∥{right arrow over (a)}−{right arrow over (b)}∥,T_(cp))is an amplitude-limited distance function; and computing the objectiveof backward edge gradient E_(edge) ^(b) comprising${{E_{edge}^{b}\left( D^{b} \right)} = {\sum\limits_{\overset{\rightarrow}{x}}{\rho_{edge}\left( {{I_{de}\left( \overset{\rightarrow}{x} \right)} - {I_{se}\left( {\overset{\rightarrow}{x} + {{\overset{\rightarrow}{d}}^{b}\left( \overset{\rightarrow}{x} \right)}} \right)}} \right)}}},$wherein ρ_(edge)(s)=min(λ_(edge)|s|,T_(edge)).
 18. The image morphingmethod according to claim 1, wherein generating the intermediate imagesequence comprises: computing the minimal value of the total objectivefunction E(D^(f),D^(b)) to obtain a specific forward morphing function

D^(f) and a specific backward morphing function

^(b); computing a forward transition image sequence I_(si)({right arrowover (x)}) and a backward transition image sequence I_(di)({right arrowover (x)}′) by using the specific forward morphing function

^(f) and the specific backward morphing function

^(b); and conducting a color-blending operation on the forwardtransition image sequence I_(si)({right arrow over (x)}) and thebackward transition image sequence I_(di)({right arrow over (x)}′) togenerate the intermediate image sequence.
 19. The image morphing methodaccording to claim 18, wherein the method of computing the forwardtransition image sequence I_(si)({right arrow over (x)}) and thebackward transition image sequence I_(di)({right arrow over (x)}′)comprises: conducting an interpolation operation on the source imageI_(s)({right arrow over (x)}) by using the specific forward morphingfunction

^(f) to obtain the forward transition image sequence I_(si)({right arrowover (x)}); and conducting an interpolation operation on the destinationimage I_(d)({right arrow over (x)}′) by using the specific backwardmorphing function

^(b) to obtain the backward transition image sequence I_(di)({rightarrow over (x)}′).
 20. An apparatus for generating intermediate imagesequence for image morphing, suitable for receiving a source image and adestination image, comprising: a unit of computing edge gradientparameter, for computing an edge gradient parameter according to asource image and a destination image; a unit of computing totalobjective function, for computing a total objective function accordingto an edge gradient parameter; and a unit of generating intermediateimage sequence, for generating the intermediate image sequence accordingto the total objective function.
 21. The apparatus for generatingintermediate image sequence for image morphing according to claim 20,further comprises: a unit of specifying and marking control points forspecifying and marking at least a control point respectively in thesource image and the destination image.